In 1994, immediately following the Expos' departure, the Rapids moved to Jamestown and assumed the name “Jamestown Jammers.”[2] The Jamestown Expos had left the city after the 1993 season, relocating to Vermont. The new team was named the "Jammers" after a fan vote, with the winning name beating out others such as the All-Americans, Furniture Makers, Jimmies, Lakers, Lucys, Muskies and Steamers.[3] The team's logo was a Tasmanian Devil-esque character. The mascot was a similar character named J.J. Jammer.

In the off-season before the 2006 season, in an attempt to put an end once and for all to the "what is a Jammer?" questions, the Jammers changed their logo to a cartoon grape theme. The new logo represents the strong tradition of grape-growing in Chautauqua County. On June 19, 2006, the eve of opening day, the team officially announced the name of its new mascot: Bubba Grape, the Baseball Ape.

Although Rich also owns the Buffalo Bisons, a higher-level minor league baseball team in the same media market, he never affiliated the two teams with the same parent club during the Jammers' time in Jamestown, and as a result, the two teams have always been in separate farm systems.

Published reports released in March 2013 (and reiterated in August 2014)[5] indicated that the Jammers were the leading candidate for relocation after the league announced it would be relocating one of its franchises to the campus of West Virginia University in Morgantown, West Virginia in 2015.[6] The team's new name, the West Virginia Black Bears, was selected shortly after the Jammers' last game.

Rich, who will continue to own the team, confirmed the news in a press conference on August 25, 2014, as did officials from the city of Jamestown, who indicated that the New York-Penn League had been trying to get out of Jamestown for several years (the league had been in the city continuously since 1960 and intermittently since the league's launch in 1939, long after nearby cities such as Bradford, Olean and Wellsville had lost their pro teams). Rich Baseball still has one year remaining on its lease with Diethrick Park, and it is unknown how the team will fulfill the terms of the lease.[7] Attendance declines were a major factor in the team's departure; the team averaged less than 800 fans per game in 2014 and had lost half of its attendance in the past five years.[8]

* – The Jammers and Batavia Muckdogs finished in a virtual tie for first place in the Pinckney Division in the 2008 season; however, the Muckdogs played two fewer games, finishing at 46–28 to the Jammers' 47–29. The Muckdogs' .622 winning percentage gave them the division title over the Jammers' .618.[9]